1. Technical Field
The present invention relates to a projection apparatus, a projection method and a projection program medium.
2. Related Art
There is generally known a projector that is an image projection apparatus that projects an image based on image data output from a personal computer or the like onto a projection target such as a screen.
When the optical axis of projection light of the projector is perpendicular to the projection plane of the projection target such as a screen, no distortion is caused in the projected image. If the optical axis is not perpendicular to the projection plane, however, owing to the installation angle of the projector, distortion is caused in the image.
Thus, as disclosed in JP 2001-339671 A, for example, a correction function typically called a trapezoid correction function for correcting distortion in an image is embedded in the projector. The distortion correction function is to correct distortion of a projected image on the basis of the angle (vertical angle) in the direction perpendicular to the horizontal plane of the optical axis and the angle (horizontal angle) in the horizontal direction that are obtained by a predetermined technique.
The principle of the distortion correction will be described with reference to FIG. 9. Herein, v and h are used as parameters of the angles. The angle v is an angle of a projector 1 in the direction perpendicular to the horizontal plane, and the angle h is an angle (direction) of the projector 1 in the horizontal direction. Note that a projection target (screen 2) is perpendicular to the horizontal plane. A horizontal base 3 is a base parallel to the horizontal plane. The x axis, y axis, and z axis express a projector coordinate system, in which the z axis is coincident with the optical axis of a projector optical system.
FIGS. 10A to 10C are detail views illustrating the relations between the projector coordinate system and the two angles h and v in FIG. 9 in this case.
Three solid arrows in FIG. 10A represent the projector coordinate system.
First, the projector 1 is rotated about the y axis as the rotation axis by the angle h that is a first angle in the direction of the arrows in the horizontal direction. As a result, the z axis and the x axis move to axes represented by dashed arrows.
Three solid arrows in FIG. 10B represent the projector coordinate system resulting from rotating the projector 1 by the angle h in the horizontal direction.
Next, the projector 1 is rotated about the x axis as the rotation axis by the angle v that is a second angle in the direction of the arrows in the vertical direction. As a result, the z axis and the y axis move to axes represented by dashed arrows.
Three arrows in FIG. 10C represent the projector coordinate system resulting from rotating the projector 1 first by the angle h in the horizontal direction and then by the angle v in the vertical direction. In this case, the x axis is parallel to the horizontal base 3.
As described above, the z-axis direction, that is, the optical axis direction (projecting direction) of the projector optical system can be arbitrarily changed by using the angles h and v.
When the projector 1 is placed as illustrated in FIG. 9, a projected image that is supposed to be displayed in a rectangular shape is displayed in a distorted quadrangular shape as represented by an uncorrected distorted quadrangle abcd on the screen 2.
Note that FIG. 9 illustrates a state in which the z axis of the projector 1 is first turned horizontally rightward by the angle h=30° and then turned vertically upward by the angle v=30°.
The distortion correction is a technique of setting a corrected rectangle a′b′c′d′ represented by a white rectangle inside of an uncorrected distorted quadrangle abcd and performing projective transformation on input image information into the corrected rectangle a′b′c′d′.
FIG. 11 is a diagram illustrating relations between the uncorrected distorted quadrangle and the corrected rectangle before and after such distortion correction of the projector 1 as viewed on the projection plane; and FIG. 12 is a diagram illustrating such relations as viewed on the surface of an output display device (such as a micromirror display device or a liquid crystal device).
In FIG. 11, a white rectangle represents the corrected rectangle a′b′c′d′, which is an image effective part. A hatched part represents an image ineffective part remaining after cutting out the corrected rectangle a′b′c′d′ from the uncorrected distorted quadrangle abcd. A point k represents a position on the projection plane through which the optical axis of the projector optical system passes.
A hatched part and a white quadrangle in FIG. 12 correspond to the hatched part and the white rectangle in FIG. 11, respectively. A percentage in a white quadrangle represents the pixel usage of the output display device. The quadrangle at the center where h=v=0 represents a case in which no distortion correction is performed and the pixel usage in this case is 100%.
There are multiple cutting-out methods in distortion correction, and FIGS. 11 and 12 illustrate an example employing a cutting-out method with which the pixel usage is improved while the aspect ratio (width÷height) of the image is remained.
The specification of the projector includes the aspect ratio of the output display device being 16:9 (approximately 1.78), the throw ratio being approximately 0.92, and the position of the optical axis of the output display device being approximately 20% higher than the height of the output display device from the center of the lower side. Note that the throw ratio is expressed by (throw ratio)=(width of projected image)÷(projection distance), and that the condition of the throw ratio is when no distortion correction is conducted.
Such distortion correction as described above is based on the assumption that the balance in right and left heights of the projector 1 so that the projector 1 is installed in a state in which no roll is caused, that is, in a state in which the projector 1 is not rotating about the optical axis. Thus, if a roll is caused, the projector 1 first needs to be adjusted and set into the state in which no roll is caused before performing distortion correction. The distortion correction is therefore not very flexible.